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Voting Squared: Quadratic Voting in Democratic Politics Eric A University of Chicago Law School Chicago Unbound Coase-Sandor Working Paper Series in Law and Coase-Sandor Institute for Law and Economics Economics 2014 Voting Squared: Quadratic Voting in Democratic Politics Eric A. Posner E. Glen Weyl Follow this and additional works at: https://chicagounbound.uchicago.edu/law_and_economics Part of the Law Commons Recommended Citation Eric Posner & E. Glen Weyl, "Voting Squared: Quadratic Voting in Democratic Politics" (Coase-Sandor Institute for Law & Economics Working Paper No. 657, 2014). This Working Paper is brought to you for free and open access by the Coase-Sandor Institute for Law and Economics at Chicago Unbound. It has been accepted for inclusion in Coase-Sandor Working Paper Series in Law and Economics by an authorized administrator of Chicago Unbound. For more information, please contact [email protected]. CHICAGO COASE-SANDOR INSTITUTE FOR LAW AND ECONOMICS WORKING PAPER NO. 657 (2D SERIES) Voting Squared: Quadratic Voting in Democratic Politics Eric A. Posner and E. Glen Weyl THE LAW SCHOOL THE UNIVERSITY OF CHICAGO February 2014 This paper can be downloaded without charge at: The University of Chicago, Institute for Law and Economics Working Paper Series Index: http://www.law.uchicago.edu/Lawecon/index.html and at the Social Science Research Network Electronic Paper Collection. Voting Squared: Quadratic Voting in Democratic Politics Eric A. Posner & E. Glen Weyl1 February 14, 2014 Abstract. Conventional democratic institutions aggregate preferences poorly. The norm of one-person-one-vote with majority rule treats people fairly by giving everyone an equal chance to influence outcomes, but fails to give proportional weight to people whose interests in a social outcome are stronger than those of other people—a problem that leads to the familiar phenomenon of tyranny of the majority. Various institutions that have been tried or proposed over the years to correct this problem— including supermajority rule, weighted voting, cumulative voting, “mixed constitutions,” executive discretion, and judicially protected rights—all badly misfire in various ways, for example, by creating gridlock or corruption. This paper proposes a new form of political decision-making based on the theory of quadratic voting. It explains how quadratic voting solves the preference aggregation problem by giving proper weight to preferences of varying intensity, how it can be incorporated into political institutions, and why it should improve equity. Introduction Groups frequently make collective decisions through majority rule. Legislators pass bills by majority; shareholders make most corporate decisions by (share-weighted) majority rule, as do directors; clubs, university faculties, and civic associations typically use majority rule as well. The reason that they do so is not entirely clear. Majority rule seems fair—and certainly fairer than rule by one (dictatorship) or a minority—but it is not obviously fairer than rule by unanimity or consensus, or rule by a supermajority like two-thirds. Majority rule has some useful properties but it often fails to advance the good of the group. 1 Kirkland & Ellis Distinguished Service Professor, University of Chicago Law School; Assistant Professor of Economics, University of Chicago. Thanks to Fabrizio Cariani, Ben Laurence, Daryl Levinson, Jonathan Masur, Philip Pettit, Sparsha Saha, Adrian Vermeule, and participants at workshops at the University of Chicago Law School and St. John’s Law School, for helpful comments, and to Matthew Brincks, Siobhan Fabio, John Moynihan, Michael Olijnyk, Tim Rudnicki, and Robert Sandoval for research assistance. The basic problem with majority rule is well-known: majorities can disregard the legitimate interests of minorities. Imagine, for example, that a community is trying to decide whether to devote funds collected from taxes to build a park. A large minority, including elderly people and families with young children, would benefit greatly from a park; a bare majority doesn’t have strong views but on balance doesn’t want to spend the money. The majority can block the park even if the minority gains more from the park than the majority loses: there is no mechanism for ensuring that the majority takes into account the minority’s disproportionate interests. For example, if the minority consists of 10,000 people who value the park at $100 each, and the majority consists of 11,000 people who disvalue the park at $2 each, the majority prevails even though the park generates a net social product of $978,000. More troublesome examples are easy to imagine and occur throughout history. In politics, majority rule— unrestricted by constitutional protections—permits the majority to expropriate the property of the minority, throw them in jail, and deprive them of the franchise. Even when the majority respects basic rights, it may deprive minorities of benefits and privileges that are available to others. The most prominent example from recent years, which we discuss in some numerical detail below, is the claim that the majority of Americans in various states unfairly deny the legal benefits of marriage to same-sex couples. The possibility that the majority may disregard the interests of the minority has a well-known label: it is “tyranny of the majority.”2 But what is wrong with tyranny of the majority? One could argue that tyranny of the majority is just a negative label for “democracy,” a label wielded by special interests, privileged groups, and others who fear majority rule. If all citizens are equal, what could be fairer than allowing the majority of them to determine policy, either directly or through representatives?3 2 The concept of tyranny of the majority is as old as majority rule, as will be discussed; early users of the phrase include John Adams, Alexis de Tocqueville, who popularized it, and John Stuart Mill, among others. John Adams, A Defence of the Constitutions of Government of the United States of America, Vol. 3, reprinted in The Works of John Adams 6 (Charles Francis Adams ed. 1851) (1788); Alexis de Tocqueville, Democracy in America (Arthur Goldhammer trans., Penguin Putnam 2004) (1835); John Stuart Mill, On Liberty (David Bromwich & George Kateb eds., Yale University Press 2003) (1859). Many formulations of it exist, of course, e.g.: Thomas Paine, Dissertations on Government; the Affairs of the Bank; and Paper Money (1786) (“despotism may be more effectually acted by many over a few than by one man over all”). 3 A number of theorems illustrate the attractive features of majority rule but show that it achieves good social outcomes only under narrow conditions. See, e.g., Howard R. Bowen, The Interpretation of Voting in the Allocation of Economic Resources, 27 Q. J. Econ. 58 (1943); Kenneth O. May, A Set of Independent Necessary and Sufficient Conditions for Simple Majority Decisions, 20 Econometrica 680 (1952); Douglas W. Rae, Decision-Rules and Individual Values in Constitutional Choice, 63 Amer. Pol. Sci. Rev. 40 (1969); Michael J. Taylor, Proof of a 2 But there are good reasons to be worried about tyranny of the majority. The first reason is that, as noted, majority rule, unless constrained to prevent tyranny of the majority, will not necessarily advance the public good. Majority rule can lead to the systematic transfer of wealth or resources from a minority to the majority. From the standpoint of the public interest, such systematic transfers are sometimes justified (for example, transfers from rich to poor), but they need not be, and nothing about majority rule guarantees that such transfers will promote public well-being. The transfers may go from one morally arbitrary group to another—for example, election winners to election losers, or poorer people to wealthier people, or black people to white people. Often these transfers incur substantial waste both administratively and in separating goods from the owners that most value them.4 Moreover, because the harm from being trapped in a minority is so great, people will struggle to form coalitions that constitute a majority—a high-stakes game that consumes time and resources that could be more productively spent elsewhere. There are actually two distinct problems here that are often merged together. In the United States, tyranny of the majority usually refers to the systematic and repeated use of the political process by a relatively stable majority (such as white people) to pass legislation that benefits it at the expense of a “discrete and insular” minority (such as black people).5 It is sometimes thought that majority rule is less troublesome when groups “take turns” playing a role in the majority. For example, if whites and Latinos outvote African-Americans on a bill proposed this year, but then African-Americans have a chance to form a coalition with Latinos to outvote whites next year, and so on, one might believe that “tyranny of the majority” does not take place. But whatever label one uses, majority rule is still not optimal. The reason is that if the white-Latino coalition inefficiently expropriates from African-Americans in year 1 by using inefficient legislation that reduces public welfare, and the black-Latino coalition does the Theorem on Majority Rule, 14 Beh. Sci. 228 (1969); Ted C. Bergstrom, When Does Majority Rule Supply Public Goods Efficiently?, 81 Scand. J. of Econ. 216 (1979). The large literature on voting rules is surveyed in Dennis C. Mueller, Public Choice III (2003); Kenneth A. Shepsle, Analyzing Politics (2d. ed. 2010); and other volumes. Lurking in the background is Arrow’s theorem, which proves that under relatively broad conditions, no voting system can produce outcomes that are both Pareto-efficient and non-dictatorial. Arrow’s theorem assumes ordinal preferences; the quadratic voting system we discuss below does not. 4 There are countless historical examples of the violent transfer of resources from a minority group to the majority; the expropriation of assets of Jewish citizens by the Nazi government in Germany is the canonical example, See Constance Harris, The Way Jews Lived: Five Hundred Years of Printed Words and Images 328 (2009).
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